PROPERTIES OF DERIVATIVE EXPANSION APPROXIMATIONS TO THE RENORMALIZATION-GROUP

Approximation only by derivative (or more generally momentum) expansio ns, combined with reparametrization invariance, turns the continuous r enormalization group into a set of partial differential equations whic h at fixed points become nonlinear eigenvalue equations for the anomal ous scaling dimension eta. We review how these equations provide a pow erful and robust means of discovering and approximating non-perturbati ve continuum limits. Gauge fields are briefly discussed. Particular em phasis is placed on the role of reparametrization invariance, and the convergence of the derivative expansion is addressed.